The kind of LCD you are referring to when mentioning calculators or old portable consoles (like the Nintendo GameBoy) is called a "reflective LCD". These displays do not have a backlight, but depend on reflecting the light that comes from the front side. They have the clear advantage over back-lit LCDs that they work perfectly in bright sunlight, because they automatically get brighter when the outside light gets brighter.
Modern LCDs on the other hand rely on backlight which is transmitted just once through the matrix (transmissive LCD). They have the clear advantage over reflective LCDs that they work well in low-light situations. The color filtering to create the red, green and blue subpixels can happen between the backlight and the matrix. Even though these displays are not meant to be used in reflective mode (backlight turned off, image generated from reflected incoming light), they often also work in that mode, although quite badly. This is why the suggestion to "illuminate the display with a flashlight" to see whether the backlight is broken or the display doesn't work at all still works today with most LCD displays.
When filming a movie, you often have very bright studio lighting to allow for high quality imaging on the film material. This lighting might be so bright that it overpowers the backlight on that PowerBook so much that the transmissive part of the LCD is miniscule compared to the reflected studio lighting. So the unintended reflective properties of the display get filmed, whereas the intended transmissive part is no longer relevant.
If you happen to have an old color LCD, like the one in the PowerBook 520c at hand, you can try to reproduce the effect by taking the laptop into bright sunshine and check whether the display starts looking like in the movie.